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CONVERGENCE ANALYSIS OF PARAREAL ALGORITHM BASED ON MILSTEIN SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS

Liying Zhang1, Jing Wang1, Weien Zhou2, Landong Liu1, Li Zhang3   

  1. 1. School of Mathematical Science, China University of Mining and Technology, Beijing 100083, China;
    2. National Innovation Institute of Defense Technology, Chinese Academy of Military Science, Beijing 100101, China;
    3. Department of Foundation Courses, Beijing Union University, Beijing 100101, China
  • Received:2018-05-07 Revised:2018-12-04 Online:2020-05-15 Published:2020-05-15
  • Supported by:

    We are very grateful to the reviewers for reading our paper carefully and providing many useful comments and suggestions. The first author is supported by NNSFC (Nos. 11601514, 11771444, 11801556 and 11971458). The fourth author is supported by Beijing Nature Science Foundation (No. 1152002). This work is also supported by NSF of Jiangsu Province of China (BK. 20130779).

Liying Zhang, Jing Wang, Weien Zhou, Landong Liu, Li Zhang. CONVERGENCE ANALYSIS OF PARAREAL ALGORITHM BASED ON MILSTEIN SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS[J]. Journal of Computational Mathematics, 2020, 38(3): 487-501.

In this paper, we propose a parareal algorithm for stochastic differential equations (SDEs), which proceeds as a two-level temporal parallelizable integrator with the Milstein scheme as the coarse propagator and the exact solution as the fine propagator. The convergence order of the proposed algorithm is analyzed under some regular assumptions. Finally, numerical experiments are dedicated to illustrate the convergence and the convergence order with respect to the iteration number k, which show the efficiency of the proposed method.

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